An algebraic system $X$ is constructed by using the known loop $\widetilde{A}_{1}$. Then a new isospectral problem is established by taking advantage of $X$, which is devoted to working out the well-known Volterra lattice hierarchy. And an extended algebraic system $\widetilde{X}$ of $X$ is presented, from which the integrable coupling systems of the Volterra lattice is obtained.
